U.S. patent number 7,576,832 [Application Number 11/417,212] was granted by the patent office on 2009-08-18 for lithographic apparatus and device manufacturing method.
This patent grant is currently assigned to ASML Netherlands B.V.. Invention is credited to Ramidin Izair Kamidi, Rob Tousain, Yin Tim Tso.
United States Patent |
7,576,832 |
Kamidi , et al. |
August 18, 2009 |
Lithographic apparatus and device manufacturing method
Abstract
A lithographic apparatus includes a movable object and a control
system to control the position of the movable object. The control
system includes a position measurement system configured to measure
the position of the movable object, a comparative unit configured
to generate a servo error signal by subtracting a position signal
representative of an actual position of the movable object from a
reference signal, a control unit configured to generate a first
control signal based on the servo error signal, a feed-forward unit
configured to generate a feed-forward signal based on the reference
signal, an addition unit configured to generate a second control
signal by adding the first control signal and the feed-forward
signal, and an actuator unit configured to actuate the movable
object. A gain of the feed-forward unit is dependent on the
position of the movable object.
Inventors: |
Kamidi; Ramidin Izair
(Eindhoven, NL), Tso; Yin Tim (Eindhoven,
NL), Tousain; Rob (Eindhoven, NL) |
Assignee: |
ASML Netherlands B.V.
(Veldhoven, NL)
|
Family
ID: |
38660893 |
Appl.
No.: |
11/417,212 |
Filed: |
May 4, 2006 |
Prior Publication Data
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|
|
|
Document
Identifier |
Publication Date |
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US 20070258079 A1 |
Nov 8, 2007 |
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Current U.S.
Class: |
355/53; 355/72;
355/75; 700/121; 700/45 |
Current CPC
Class: |
G03F
7/70725 (20130101) |
Current International
Class: |
G03B
27/42 (20060101) |
Field of
Search: |
;355/53,72,75 ;318/649
;700/45,121 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
2005 IEEE Conference on Control Applications, Aug. 28-31, 2005,
Toronto, Canada, TC 1.6, Metthijs Boerlage, Maarteen Steinbuch,
Georgo Angelis: "Frequency response based multivariable control
design for motion systems". cited by examiner .
Control Engineering Practice 13, Feb. 2005, p. 145-157, Paul
Lambrechts, Matthijs Boerlage, Maarteen Steinbuch: "Trajectory and
feed forward design for electrochemical motion systems". cited by
examiner .
2004 American Control Conference, Jun. 30-Jul. 2, 2004, Boston
Massachusetts, FrM09.4, Matthijs Boerlage, Rob Tousain, Maarten
Steinbuch: "Jerk derivative feed forward control for motion
systems". cited by examiner .
Control engineering Practice 10, 2002, p. 739-755, Marc van de Wal,
Gregor van Baars, Frank Sperling, Okko Bosgra: "Multivariable
H.sub.--inf/mu feedback control design for high-precision wafer
stage motion". cited by examiner.
|
Primary Examiner: Lee; Diane I
Assistant Examiner: Whitesell-Gordon; Steven H
Attorney, Agent or Firm: Pillsbury Winthrop Shaw Pittman
LLP
Claims
What is claimed is:
1. A lithographic apparatus comprising a movable object and a
control system configured to control a position of said movable
object, said control system comprising: a position measurement
system configured to measure the position of said movable object; a
comparative unit configured to generate a servo error signal by
subtracting a position signal representative of an actual position
of said movable object from a reference signal; a control unit
configured to generate a first control signal based on said servo
error signal; a feed-forward unit configured to generate a
feed-forward signal based on said reference signal; an addition
unit configured to generate a second control signal by adding said
first control signal and said feed-forward signal; and an actuator
unit configured to actuate said movable object based on said second
control signal, wherein one or more coefficients of a function
representative of said feed-forward unit are dependent on said
position signal and/or said reference signal.
2. The lithographic apparatus of claim 1, wherein said feed-forward
unit is a multi-input multi-output (MIMO) feed-forward unit.
3. The lithographic apparatus of claim 1, wherein said one or more
coefficients comprise one or more gains of said feed-forward
unit.
4. The lithographic apparatus of claim 1, wherein said one or more
coefficients comprise one or more time constants of said
feed-forward unit.
5. The lithographic apparatus of claim 1, wherein the feed-forward
unit comprises one or more time delay units.
6. The lithographic apparatus of claim 1, wherein said feed-forward
unit is configured to generate a feed-forward signal in a first
degree of freedom based on a change in the reference signal in
another degree of freedom, wherein said feed-forward signal
compensates for deformation of said movable object in said first
degree of freedom as a result of movement of said movable object in
said other degree of freedom.
7. The lithographic apparatus of claim 1, wherein all gains of said
feed-forward unit are dependent on the position signal and/or said
reference signal.
8. The lithographic apparatus of claim 1, wherein said one or more
coefficients are determined based on at least one of a position
set-point, a derivative of said position set-point, or another
signal being dependent on said position set-point.
9. The lithographic apparatus of claim 1, wherein said feed-forward
unit generates a feed-forward signal using the second and the
fourth derivative of the reference signal.
10. The lithographic apparatus of claim 1, wherein said
feed-forward unit is configured to generate a feed-forward signal
in a first degree of freedom based on a change in the reference
signal in said first degree of freedom, wherein said feed-forward
signal compensates for deformation of said movable object in said
first degree of freedom as a result of movement of said movable
object in said first degree of freedom.
11. The lithographic apparatus of claim 1, wherein said position
measurement system is configured to measure the position of said
movable object in six degrees of freedom.
12. The lithographic apparatus of claim 1, wherein said position
measurement system is an interferometer position measurement
system.
13. The lithographic apparatus of claim 1, wherein said movable
object is a substrate stage or a reticle stage.
14. The lithographic apparatus of claim 2, wherein said control
system comprises a gain balancing unit and/or a gain scheduling
unit configured to de-couple the dynamics of said movable object in
the degrees of freedom in which said movable object is
controlled.
15. A lithographic apparatus comprising a movable object and a
control system configured to control a position of said movable
object, said control system comprising: a position measurement
system configured to measure the position of said movable object; a
comparative unit configured to generate a servo error signal by
subtracting a position signal representative of an actual position
of said movable object from a reference signal; a control unit
configured to generate a first control signal based on said servo
error signal; a feed-forward unit configured to generate a
feed-forward signal based on said reference signal; an addition
unit configured to generate a second control signal by adding said
first control signal and said feed-forward signal; and an actuator
unit configured to actuate said movable object based on said second
control signal, wherein one or more coefficients of said
feed-forward unit are dependent on said position signal and/or said
reference signal, and wherein said one or more coefficients are
determined based on at least one of the actual position of said
movable object, a derivative of said actual position, or another
signal being dependent on said actual position.
16. A device manufacturing method comprising: projecting a
patterned beam of radiation onto a substrate, and controlling a
position of a movable object, said controlling comprising
feed-forwarding a reference signal using a feed-forward unit,
wherein one or more coefficients of a function representative of
the feed-forward unit depend on said reference signal or a measured
position signal of said movable object to compensate for
deformation of said movable object.
17. The method of claim 16, wherein said feed-forward unit is a
multi-input multi-output (MIMO) feed-forward unit, that generates a
feed-forward signal in a first degree of freedom based on a change
in the reference signal in an other degree of freedom, wherein said
feed-forward signal compensates for deformation of said movable
object in said first degree of freedom as a result of movement of
said movable object in said other degree of freedom.
18. The method of claim 16, wherein said moveable object is a
substrate table configured to hold the substrate or a pattern
support configured to hold a patterning device used to form the
patterned beam of radiation.
Description
BACKGROUND
1. Field of the Invention
The present invention relates to a lithographic apparatus and a
method for manufacturing a device.
2. Description of the Related Art
A lithographic apparatus is a machine that applies a desired
pattern onto a substrate, usually onto a target portion of the
substrate. A lithographic apparatus can be used, for example, in
the manufacture of integrated circuits (ICs). In such a case, a
patterning device, which is alternatively referred to as a mask or
a reticle, may be used to generate a circuit pattern to be formed
on an individual layer of the IC. This pattern can be transferred
onto a target portion (e.g. including part of, one, or several
dies) on a substrate (e.g. a silicon wafer). Transfer of the
pattern is typically via imaging onto a layer of
radiation-sensitive material (resist) provided on the substrate. In
general, a single substrate will contain a network of adjacent
target portions that are successively patterned. Conventional
lithographic apparatus include so-called steppers, in which each
target portion is irradiated by exposing an entire pattern onto the
target portion at once, and so-called scanners, in which each
target portion is irradiated by scanning the pattern through a
radiation beam in a given direction (the "scanning"-direction)
while synchronously scanning the substrate parallel or
anti-parallel to this direction. It is also possible to transfer
the pattern from the patterning device to the substrate by
imprinting the pattern onto the substrate.
Important factors for the performance of a lithographic apparatus
are the throughput, i.e. the number of wafers that is produced
within a certain period, and the overlay, i.e. the production
quality. In the industry, there is a continuous demand to improve
the throughput and overlay of the lithographic apparatus.
In the known lithographic apparatus, the stage accuracy, which is
measured in 6 degrees of freedom and is important for overlay, is
controlled by using a combination of single input single output
(SISO) feedback and feed-forward control for each 6 axes in a two
degree of freedom controller structure. The feedback controller
guards (robust) stability and increases disturbance rejection,
while the feed-forward controller improves tracking
performance.
Generally, the higher throughput can impact the overlay
performance; higher accelerations (and jerk) cause higher internal
dynamic vibrations (or deformations) of the stages, which result in
a deterioration of the stage accuracy. The position accuracy of the
stages, especially directly after accelerating, is mainly dependent
on the accuracy of the set-point feed-forward.
As a reaction of the feedback controller, internal stage
deformations, caused by higher accelerations and jerks, result in
an overshoot, which deteriorates the settle behaviour of the
controller error. In addition to this, the magnitude of the
internal stage deformation and with this the overshoot does not
have to be the same for every position of the stage.
SUMMARY
It is desirable to provide a lithographic apparatus wherein the
throughput and/or the overlay may be improved. In particular, it is
desirable to provide a lithographic apparatus in which the motion
times of moveable objects is decreased, and in which small settling
times for the movable objects are required, so that the throughput
may be improved without sacrificing the overlay performance.
According to an embodiment of the invention, there is provided a
lithographic apparatus including a movable object and a control
system to control a position of the movable object, the control
system including: position measurement system configured to measure
the position of the movable object, a comparative unit configured
to generate a servo error signal by subtracting a position signal
representative for an actual position of the movable object from a
reference signal, a control unit configured to generate a first
control signal on the basis of the servo error signal, a
feed-forward unit configured to generate a feed-forward signal on
the basis of the reference signal, an addition unit configured to
generate a second control signal by adding the first control signal
and the feed-forward signal, and an actuator unit configured to
actuate the movable object on the basis of the second control
signal, wherein one or more coefficients of the feed-forward unit
are dependent on the position signal and/or the reference
signal.
According to an embodiment of the invention, there is provided a
device manufacturing method using a projection system for
projecting a patterned beam of radiation onto a substrate, and
including the controlling of the position of a movable object,
wherein the controlling includes the feed-forward of a reference
signal using a feed-forward unit, wherein one or more coefficients
of the feed-forward unit depend on the reference signal or a
measured position signal of the movable object to compensate for
deformation of the movable object.
BRIEF DESCRIPTION OF THE DRAWINGS
Embodiments of the invention will now be described, by way of
example only, with reference to the accompanying schematic drawings
in which corresponding reference symbols indicate corresponding
parts, and in which:
FIG. 1 depicts a lithographic apparatus according to an embodiment
of the invention;
FIG. 2 depicts schematically a top view of a substrate stage in
accordance with an embodiment of the invention,
FIG. 3 depicts a control system for a substrate stage according to
an embodiment of the invention, and
FIG. 4 depicts an embodiment of a MIMO substrate stage control
system according to an embodiment of the invention.
DETAILED DESCRIPTION
FIG. 1 schematically depicts a lithographic apparatus according to
one embodiment of the invention. The apparatus includes an
illumination system (illuminator) IL configured to condition a
radiation beam B (e.g. UV radiation or any other suitable
radiation), a mask support structure (e.g. a mask table) MT
constructed to support a patterning device (e.g. a mask) MA and
connected to a first positioning device PM configured to accurately
position the patterning device in accordance with certain
parameters. The apparatus also includes a substrate table (e.g. a
wafer table) WT or "substrate support" constructed to hold a
substrate (e.g. a resist-coated wafer) W and connected to a second
positioning device PW configured to accurately position the
substrate in accordance with certain parameters. The apparatus
further includes a projection system (e.g. a refractive projection
lens system) PS configured to project a pattern imparted to the
radiation beam B by patterning device MA onto a target portion C
(e.g. including one or more dies) of the substrate W.
The illumination system may include various types of optical
components, such as refractive, reflective, magnetic,
electromagnetic, electrostatic or other types of optical
components, or any combination thereof, for directing, shaping, or
controlling radiation.
The mask support structure supports, i.e. bears the weight of, the
patterning device. It holds the patterning device in a manner that
depends on the orientation of the patterning device, the design of
the lithographic apparatus, and other conditions, such as for
example whether or not the patterning device is held in a vacuum
environment. The mask support structure can use mechanical, vacuum,
electrostatic or other clamping techniques to hold the patterning
device. The mask support structure may be a frame or a table, for
example, which may be fixed or movable as required. The mask
support structure may ensure that the patterning device is at a
desired position, for example with respect to the projection
system. Any use of the terms "reticle" or "mask" herein may be
considered synonymous with the more general term "patterning
device."
The term "patterning device" used herein should be broadly
interpreted as referring to any device that can be used to impart a
radiation beam with a pattern in its cross-section so as to create
a pattern in a target portion of the substrate. It should be noted
that the pattern imparted to the radiation beam may not exactly
correspond to the desired pattern in the target portion of the
substrate, for example if the pattern includes phase-shifting
features or so called assist features. Generally, the pattern
imparted to the radiation beam will correspond to a particular
functional layer in a device being created in the target portion,
such as an integrated circuit.
The patterning device may be transmissive or reflective. Examples
of patterning devices include masks, programmable mirror arrays,
and programmable LCD panels. Masks are well known in lithography,
and include mask types such as binary, alternating phase-shift, and
attenuated phase-shift, as well as various hybrid mask types. An
example of a programmable mirror array employs a matrix arrangement
of small mirrors, each of which can be individually tilted so as to
reflect an incoming radiation beam in different directions. The
tilted mirrors impart a pattern in a radiation beam which is
reflected by the mirror matrix.
The term "projection system" used herein should be broadly
interpreted as encompassing any type of projection system,
including refractive, reflective, catadioptric, magnetic,
electromagnetic and electrostatic optical systems, or any
combination thereof, as appropriate for the exposure radiation
being used, or for other factors such as the use of an immersion
liquid or the use of a vacuum. Any use of the term "projection
lens" herein may be considered as synonymous with the more general
term "projection system".
As here depicted, the apparatus is of a transmissive type (e.g.
employing a transmissive mask). Alternatively, the apparatus may be
of a reflective type (e.g. employing a programmable mirror array of
a type as referred to above, or employing a reflective mask).
The lithographic apparatus may be of a type having two (dual stage)
or more substrate tables or "substrate supports" (and/or two or
more mask tables or "mask supports"). In such "multiple stage"
machines the additional tables or supports may be used in parallel,
or preparatory steps may be carried out on one or more tables or
supports while one or more other tables or supports are being used
for exposure.
The lithographic apparatus may also be of a type wherein at least a
portion of the substrate may be covered by a liquid having a
relatively high refractive index, e.g. water, so as to fill a space
between the projection system and the substrate. An immersion
liquid may also be applied to other spaces in the lithographic
apparatus, for example, between the mask and the projection system.
Immersion techniques can be used to increase the numerical aperture
of projection systems. The term "immersion" as used herein does not
mean that a structure, such as a substrate, must be submerged in
liquid, but rather only means that a liquid is located between the
projection system and the substrate during exposure.
Referring to FIG. 1, the illuminator IL receives a radiation beam
from a radiation source SO. The source and the lithographic
apparatus may be separate entities, for example when the source is
an excimer laser. In such cases, the source is not considered to
form part of the lithographic apparatus and the radiation beam is
passed from the source SO to the illuminator IL with the aid of a
beam delivery system BD including, for example, suitable directing
mirrors and/or a beam expander. In other cases the source may be an
integral part of the lithographic apparatus, for example when the
source is a mercury lamp. The source SO and the illuminator IL,
together with the beam delivery system BD if required, may be
referred to as a radiation system.
The illuminator IL may include an adjuster AD configured to adjust
the angular intensity distribution of the radiation beam.
Generally, at least the outer and/or inner radial extent (commonly
referred to as .sigma.-outer and .sigma.-inner, respectively) of
the intensity distribution in a pupil plane of the illuminator can
be adjusted. In addition, the illuminator IL may include various
other components, such as an integrator IN and a condenser CO. The
illuminator may be used to condition the radiation beam, to have a
desired uniformity and intensity distribution in its
cross-section.
The radiation beam B is incident on the patterning device (e.g.,
mask MA), which is held on the mask support structure (e.g., mask
table MT), and is patterned by the patterning device. Having
traversed the mask MA, the radiation beam B passes through the
projection system PS, which focuses the beam onto a target portion
C of the substrate W. With the aid of the second positioning device
PW and position sensor IF (e.g. an interferometric device, linear
encoder or capacitive sensor), the substrate table WT can be moved
accurately, e.g. so as to position different target portions C in
the path of the radiation beam B. Similarly, the first positioning
device PM and another position sensor (which is not explicitly
depicted in FIG. 1) can be used to accurately position the mask MA
with respect to the path of the radiation beam B, e.g. after
mechanical retrieval from a mask library, or during a scan. In
general, movement of the mask table MT may be realized with the aid
of a long-stroke module (coarse positioning) and a short-stroke
module (fine positioning), which form part of the first positioning
device PM. Similarly, movement of the substrate table WT or
"substrate support" may be realized using a long-stroke module and
a short-stroke module, which form part of the second positioner PW.
In the case of a stepper (as opposed to a scanner) the mask table
MT may be connected to a short-stroke actuator only, or may be
fixed. Mask MA and substrate W may be aligned using mask alignment
marks M1, M2 and substrate alignment marks P1, P2. Although the
substrate alignment marks as illustrated occupy dedicated target
portions, they may be located in spaces between target portions
(these are known as scribe-lane alignment marks). Similarly, in
situations in which more than one die is provided on the mask MA,
the mask alignment marks may be located between the dies.
The depicted apparatus could be used in at least one of the
following modes:
1. In step mode, the mask table MT or "mask support" and the
substrate table WT or "substrate support" are kept essentially
stationary, while an entire pattern imparted to the radiation beam
is projected onto a target portion C at one time (i.e. a single
static exposure). The substrate table WT or "substrate support" is
then shifted in the X and/or Y direction so that a different target
portion C can be exposed. In step mode, the maximum size of the
exposure field limits the size of the target portion C imaged in a
single static exposure.
2. In scan mode, the mask table MT or "mask support" and the
substrate table WT or "substrate support" are scanned synchronously
while a pattern imparted to the radiation beam is projected onto a
target portion C (i.e. a single dynamic exposure). The velocity and
direction of the substrate table WT or "substrate support" relative
to the mask table MT or "mask support" may be determined by the
(de-)magnification and image reversal characteristics of the
projection system PS. In scan mode, the maximum size of the
exposure field limits the width (in the non-scanning direction) of
the target portion in a single dynamic exposure, whereas the length
of the scanning motion determines the height (in the scanning
direction) of the target portion.
3. In another mode, the mask table MT or "mask support" is kept
essentially stationary holding a programmable patterning device,
and the substrate table WT or "substrate support" is moved or
scanned while a pattern imparted to the radiation beam is projected
onto a target portion C. In this mode, generally a pulsed radiation
source is employed and the programmable patterning device is
updated as required after each movement of the substrate table WT
or "substrate support" or in between successive radiation pulses
during a scan. This mode of operation can be readily applied to
maskless lithography that utilizes programmable patterning device,
such as a programmable mirror array of a type as referred to
above.
Combinations and/or variations on the above described modes of use
or entirely different modes of use may also be employed.
The substrate stage is a relative stiff body which has to be moved
quickly and with great accuracy to obtain the throughput and
overlay desired in modern lithography application. However, as
demands on throughput and overlay performance are increasing, the
stage has to be moved with increasing acceleration without losing
overlay performance in order to decrease motion times. Due to the
high accelerations, the stage may deform during the acceleration.
These internal stage deformations may result in an overshoot which
deteriorates the settle behaviour of the substrate stage. This
effect of the internal deformations will hereinafter further be
explained with reference to FIG. 2.
FIG. 2 depicts a schematic top view of a substrate stage
represented as a mass-spring system. The mass Ma represents a part
of the substrate stage on which the actuator is mounted and the
mass Ms represents the rest of the stage. Two springs connect the
two masses of the stage. An interferometer Ifx is capable of
measuring the x-position of the substrate stage, in particular the
mass Ms, and an interferometer Ify is capable of measuring the
y-position of the substrate stage, in particular the mass Ms.
In practice, the substrate stage will not behave as a mass spring
system having two masses connected by springs, but the mechanics
are much more complex. However, as the point where the substrate
stage is actuated and the point where the position of the substrate
stage is measured are located on different masses Ma and Ms,
respectively, the schematic representation as a mass-spring system
suffices to explain the effect of internal deformations on the
settling behaviour.
When it is desired to move the stage in the direction of arrow A
(x-direction), for instance for a scanning movement, the reference
signal will be adapted accordingly in order to accelerate the
substrate stage in the x-direction. As the actuator mass Ma is
directly coupled to the actuator, this mass Ma will directly follow
the (change in the) reference signal. This movement is for example
indicated by the dashed line in FIG. 2.
However, the mass Ms which is connected via the springs to the mass
Ma, will not directly follow the change in the reference signal,
but will have some lag due to the presence of the springs. Also,
the mass Ms may rotate with respect to the mass Ma due to the
presence of the springs. The lag and the rotation of the mass Ms
are representative for the internal deformations within the
stage.
The controller will notice the lag and rotation as the
interferometer Ifx measures the x-position of the mass Ms rather
than the position of the mass Ma. Thus, since the controller
notices the lag, it will actuate mass Ma in order to compensate for
the lag/rotation of mass Ms of which the x-position is measured. As
this (over)compensation is not necessary, since the mass Ma already
correctly follows the reference signal and the error signal is
caused by the (temporary and elastic) internal deformation in thee
substrate stage, this (over)compensation will result in an
overshoot and as a consequence in a longer settling time. Thus, as
a consequence of the internal deformations in the substrate stage,
the controller may have a deteriorating effect on the settling time
of the substrate stage.
Furthermore, it can be seen in FIG. 2 that the actual x-position of
Ms measured by the interferometer Ifx depends on the position of
the substrate stage in the y-direction. At the level on which the
interferometer Ifx measures in FIG. 2 the actual x-position of the
substrate stage (dashed line), the difference between the
x-position of the mass Ma and the mass Ms is relatively large. This
difference would be smaller when the interferometer Ifx would
measure the x-position of the mass Ms at the level indicated with
an arrow B. The latter would for instance be the case if the stage
would be moved over a certain distance in the y-direction (to the
top side of the drawing) before starting the movement indicated by
the arrow A.
In general the position of the interferometer is stationary. Thus,
upon movement of the substrate stage the position of the substrate
stage is measured at different locations on this substrate stage.
At these locations different internal deformations may occur. As
the amount of internal deformation at a certain location in the
substrate stage has an influence on the actual position measured at
that location, the position of the substrate stage, in particular
the position of the substrate stage with respect to the location of
the respective interferometer Ifx, is relevant for compensating the
error which is measured due to the internal deformation.
The position of the mass Ms in the y-position is measured by Ify.
Due to the acceleration of Ma as a result of a change in the
reference signal in the x-direction, the mass Ms rotates. Although
the rotation is temporarily and the intended movement of the
substrate stage is only in the x-direction, the interferometer Ify
measures a change in the actual y-position of the mass Ms. The
controller will send a control signal to the actuator to compensate
for this change in the y-position. However, as the system itself
also compensates for the elastic deformation, the controller signal
result in an overshoot and longer settling time in the
y-direction.
Furthermore, due to the rotation of the mass Ms, also the
measurement of the actual position of the substrate stage in the
y-direction is dependent on the position of the substrate stage
with respect to the interferometer Ify. The interferometer Ify
measures the dashed line of the mass Ma as the actual y-position of
the substrate stage. At this location a large change of the actual
y-position of the mass Ms is measured. However, when the
interferometer would be located (in the drawing) more to the right
side, or the substrate stage would be positioned more to the left
the error, determined in the y-direction would be less as the
effect of the rotation/deformation is smaller at that location.
Thus, also in another direction (degree of freedom) as the
direction in which a movement is made, the actual position measured
by the respective interferometer in that other direction may be
influenced due to internal deformations of the substrate stage,
whereby this influence may be position dependent.
In an embodiment of the present invention, there is provided a
position control system to deal with one or more of the above
situations due to internal deformations of the substrate stage
during (large) accelerations, and therewith to avoid overshoot and
increasing settling times. Two embodiments of such position control
system are shown in FIGS. 3 and 4. These embodiment will be
described hereinafter.
In FIG. 3, a position control system according to an embodiment of
the invention is shown. At the left side of the drawing a set-point
or reference signal generator is shown. This set-point generator
provides several reference signals to the control system which are
representative of the desired position of the substrate stage, or
derivatives thereof. The controller unit is represented by C(s) and
the mechanics of the substrate stage is represented by P(s).
A servo error signal is fed to the controller unit C(s). This servo
error signal is the difference between the position reference
signal rpos and the actual position of the substrate stage measured
by the position measurement system, for instance an interferometer
system. This servo error signal is generated by a comparative unit.
The position measurement system measures the position of the
substrate stage in six degrees of freedom DOF. The control system
is a combination of six SISO control systems, one for each degree
of freedom.
A reference signal is fed to the feed-forward unit Kf(rpos). This
reference signal may be any signal which is useful to represent the
acceleration and/or deformation of the substrate stage. In a
preferred embodiment the second and fourth derivative of the
reference position signal are used, i.e. the acceleration and snap.
However, any other suitable signal such as velocity, jerk and crack
(first, third and fifth derivative of the reference position
signal) may also be used. The feedforward signal output by the
feedforward is added to the output of the controller unit with an
addition unit. The output of the addition unit is fed to the
mechanics of the substrate stage represented by P(s)
The gains or more generally the coefficients of the feed-forward
unit are made dependent on the position of the substrate stage.
This position of the substrate stage is, as shown in FIG. 3,
brought into the feed-forward unit by feeding the reference
position signal to the feed-forward unit. As a result of the
relative large scale on which the effects of the position
dependence of the substrate stage occur, the possible difference
between reference position signal and actual position signal does
not have a large influence on the effect of the position dependent
feed-forward. In alternative embodiments one or more gains or
coefficients of the feed-forward unit may be determined based on
derivatives of the position reference signal, such as speed,
acceleration, jerk, snap, crack and such, and/or other signals
being dependent on the position set-point, possibly in combination
with the position reference signal. Also, one or more gains or
coefficients of the feed-forward unit may be determined on the
actual position of the movable object, a derivative thereof, and/or
another signals being dependent on the actual position of the
movable object. In yet another embodiment one or more gains are
dependent on the difference between the reference signal and the
position signal. In an embodiment, all gains of the feed-forward
unit are dependent on the position signal and/or said reference
signal.
Furthermore, instead of or in addition to the gains, other
coefficients of the feed-forward unit, such as time constants, may
depend on the reference signal and/or the position signal.
By feed-forward of the reference signal which also takes into
account the internal deformation of the substrate stage and the
location thereof by multiplying the reference signal with a certain
gain or other coefficients of the feed-forward unit which are
position dependent, the control system takes the effect of the
deformation on the measurement into account, and compensates
therefor. As a result, mass Ms instead of mass Ma will follow the
reference signal while mass Ma will actually be ahead of the
reference signal. The actual position measured by the respective
measurement system will thus match with the reference signal.
Therefore, the controller will not compensate and the overshoot and
increasing settling times resulting from the compensation will not
occur.
The control system of FIG. 3 provides a solution for the effects of
internal deformations in a single degree of freedom. However, as
explained in relation to FIG. 2, the internal deformations caused
by acceleration/movement in one degree of freedom may also result
in worse behaviour in other degrees of freedom. The position
control system of FIG. 4 may also provide a solution for this
effect.
In FIG. 4, a more advanced position control system in accordance
with an embodiment is shown. In this system, the SISO independent
position control system is replaced by a multi-input multi-output
MIMO position dependent set-point feed-forward in order to
compensate for controller errors in the non-scanning (non-movement)
axes (degrees of freedom) and for position dependent dynamics and
cross-talk in all axes, caused by internal deformations of the
substrate stage.
In this system the 6 DOF position, acceleration and snap set-points
are defined as:
##EQU00001##
The MIMO plant P(s) (in this case the substrate stage) has 6 inputs
(Fx, Fy1, Fy2, Fz1, Fz2, Fz3) and 6 outputs (xpos, ypos, Rzpos,
zpos, Rxpos, Rypos):
.function..function..function..function..function..function..function..fu-
nction..function..function. ##EQU00002##
The Gain Balancing (GB) and the Gain Scheduling (GS(rpos)) are used
to de-couple the 6 DOF MIMO plant P(s) in order to reduce cross
talk. The de-coupled mechanics may be approximated by 6 SISO
systems x/y/Rz/z/Rx/Ry, which are controlled by 6 SISO controllers
Cxx(s), Cyy(s), . . . , CryRy(s), respectively.
The difference between MIMO and SISO set-point feed-forward is that
when an axis has to follow a position set-point, in the MIMO system
feed-forward forces may be applied on all 6 axes, which are
generated using the set-points of the corresponding axis, instead
of in the SISO system only one feed-forward force in the same
axis.
If for instance a combined movement in x and y is performed,
feed-forward forces from x and y to the x/y/Rz/z/Rx/Ry axes may be
applied. As a consequence, in each degree of freedom two different
feed-forward forces may be applied, one based on the movement in
the x-direction and the other based on the movement in the
y-direction.
In an embodiment delay corrections for all 6 axes may be used for
the acceleration and snap feed-forward, possibly separately, in
order to compensate for IO delay and zero order hold. Delay
corrections may be performed using time delay units. In an
embodiment, the feedforward unit comprises one or more time delay
corrections. It is remarked that these delay corrections are not
explicitly shown in the embodiment of FIG. 4.
The following functions may be used for the position dependent
acceleration and snap feed-forward, respectively:
.function..times..function. ##EQU00003## ##EQU00003.2##
.function..times..function. ##EQU00003.3##
The acceleration parameters Kfai and snap parameters Kfsi
determined at certain positions are constant values while the
scheduling functions wi are dependent on the position rpos and may
have the following characteristics:
.times..function..ltoreq..function..ltoreq..times..times..A-inverted.
##EQU00004##
These scheduling functions can be chosen in such a way that
Kfa(rpos)/Kfs(rpos) is equal to the real position dependent snap
(for all positions) or as linear functions where the real position
dependent snap is approximated. If linear scheduling functions are
chosen then the extent in which the position dependency is
approximated is dependent on the number of acceleration parameters
Kfai and/or snap parameters Kfsi (determined at certain positions)
used for the feed-forward.
After the system is de-coupled (GB is optimized), small settling
time and thus a substantial throughput improvement of the stages,
is attained in all axes and all positions using the MIMO position
dependent set-point feed-forward with linear scheduling functions.
The controllers errors directly after acceleration are considerably
reduced which result in an overlay improvement.
Thus, with the position control system shown in FIG. 4, the effect
of internal deformations in another degree of freedom than the
degree of freedom wherein a movement/acceleration is made can be
compensated by using the MIMO feed-forward. For instance, the
possible incorrect measurement in the y-direction as described in
relation to FIG. 2 for Ify is compensated by the control system.
Upon movement of the substrate stage in the x-direction, the mass
Ma will be moved by the actuator in the y-direction so that the
mass Ms, although moved by the internal deformations with respect
to Ma, substantially remains in the y-position that matches with
the reference signal in the y-direction, during the
accelerations/movement in the x-direction. As a result, there will
be no error signal in the y-direction and the controller will not
have to provide a control signal to compensate. Therefore,
overshoot and larger settling times are substantially avoided.
It will be appreciated that the position control system, in
particular the feed-forward unit will also compensate for all other
degrees of freedom, including the degree of freedom in which the
movement is made. Thus, overshoot and larger settling times are
substantially avoided in all degrees of freedom due to the position
control system of the present invention. Therewith, the throughput
and overlay performance may substantially be improved.
The control system of FIG. 4 takes in the feed-forward unit the
position of the substrate stage into account by making the gains of
the feed-forward unit dependent on the position of the substrate
stage. However, for instance in a system wherein this position
dependence does not play a major role (substantially the same
deformations along the reflective surface of a substrate stage in
an interferometer system) or is not present (sensor on fixed
location on substrate stage), the position dependence of the gains
of the feed-forward unit may be omitted. In such system the MIMO
feed-forward unit may still be beneficial to compensate for the
internal deformations of the substrate stage.
Hereinabove, position control systems have been described for the
control of the position of a substrate stage. Similar systems may
be used to control the position of another movable object of a
lithographic apparatus with high accuracy. In particular, the
control system may be used to control the position of a reticle
stage.
The position control system may be realized as software in a
computer program, or as a hardware control system, or a combination
thereof, or any other type of suitable control system.
Although specific reference may be made in this text to the use of
lithographic apparatus in the manufacture of ICs, it should be
understood that the lithographic apparatus described herein may
have other applications, such as the manufacture of integrated
optical systems, guidance and detection patterns for magnetic
domain memories, flat-panel displays, liquid-crystal displays
(LCDs), thin-film magnetic heads, etc. The skilled artisan will
appreciate that, in the context of such alternative applications,
any use of the terms "wafer" or "die" herein may be considered as
synonymous with the more general terms "substrate" or "target
portion", respectively. The substrate referred to herein may be
processed, before or after exposure, in for example a track (a tool
that typically applies a layer of resist to a substrate and
develops the exposed resist), a metrology tool and/or an inspection
tool. Where applicable, the disclosure herein may be applied to
such and other substrate processing tools. Further, the substrate
may be processed more than once, for example in order to create a
multi-layer IC, so that the term substrate used herein may also
refer to a substrate that already contains multiple processed
layers.
Although specific reference may have been made above to the use of
embodiments of the invention in the context of optical lithography,
it will be appreciated that the invention may be used in other
applications, for example imprint lithography, and where the
context allows, is not limited to optical lithography. In imprint
lithography a topography in a patterning device defines the pattern
created on a substrate. The topography of the patterning device may
be pressed into a layer of resist supplied to the substrate
whereupon the resist is cured by applying electromagnetic
radiation, heat, pressure or a combination thereof. The patterning
device is moved out of the resist leaving a pattern in it after the
resist is cured.
The terms "radiation" and "beam" used herein encompass all types of
electromagnetic radiation, including ultraviolet (UV) radiation
(e.g. having a wavelength of or about 365, 248, 193, 157 or 126 nm)
and extreme ultra-violet (EUV) radiation (e.g. having a wavelength
in the range of 5-20 nm), as well as particle beams, such as ion
beams or electron beams.
The term "lens", where the context allows, may refer to any one or
combination of various types of optical components, including
refractive, reflective, magnetic, electromagnetic and electrostatic
optical components.
While specific embodiments of the invention have been described
above, it will be appreciated that the invention may be practiced
otherwise than as described. For example, the invention may take
the form of a computer program containing one or more sequences of
machine-readable instructions describing a method as disclosed
above, or a data storage medium (e.g. semiconductor memory,
magnetic or optical disk) having such a computer program stored
therein.
The descriptions above are intended to be illustrative, not
limiting. Thus, it will be apparent to one skilled in the art that
modifications may be made to the invention as described without
departing from the scope of the claims set out below.
* * * * *